Which of the following defines irrational numbers?

Irrational numbers are defined as numbers that cannot be expressed as a simple fraction or ratio of two integers. This means their decimal expansion is non-repeating and non-terminating. Examples of irrational numbers include the square root of 2 and pi (π).

The correct choice highlights that these numbers do not fit into the format of a/b where both a and b are integers, which is the defining characteristic of rational numbers. The understanding of irrational numbers is crucial in mathematics, as they extend the number system beyond rational numbers, encompassing a richer set of values that are critical for various applications in science, engineering, and daily life.

Other options describe characteristics that pertain to different categories of numbers. For instance, expressing numbers as fractions refers to rational numbers, while specifying whole and negative numbers pertains particularly to integers. Lastly, stating that any number with an exact decimal implies a specific type of rational number, which does not cover the concept of irrational numbers accurately.